We explore the impact of black hole spins on the dynamics of high-energy black hole collisions. We report results from numerical simulations with γ factors up to 2.49 and dimensionless spin parameter χ=+0.85, +0.6, 0, -0.6, -0.85. We find that the scattering threshold becomes independent of spin at large center-of-mass energies, confirming previous conjectures that structure does not matter in ultrarelativistic collisions. It has further been argued that in this limit all of the kinetic energy of the system may be radiated by fine tuning the impact parameter to threshold. On the contrary, we find that only about 60% of the kinetic energy is radiated for γ=2.49. By monitoring apparent horizons before and after scattering events we show that the "missing energy" is absorbed by the individual black holes in the encounter, and moreover the individual black-hole spins change significantly. We support this conclusion with perturbative calculations. An extrapolation of our results to the limit γ→∞ suggests that about half of the center-of-mass energy of the system can be emitted in gravitational radiation, while the rest must be converted into rest-mass and spin energy.